A graph theoretic approach to optimal target tracking for mobile robot teams

In this paper, we present an optimization framework for target tracking with mobile robot teams. The target tracking problem is modeled as a generic semidefinite program (SDP). When paired with an appropriate objective function, the solution to the resulting problem instance yields an optimal robot configuration for target tracking at each time-step, while guaranteeing target coverage (each target is tracked by at least one robot) and maintaining network connectivity. Our methodology is based on the graph theoretic result where the second smallest eigenvalue of the interconnection graph Laplacian matrix is a measure for the connectivity of the graph. This formulation enables us to model agent-target coverage and inter-agent communication constraints as linear-matrix inequalities. We also show that when the communication constraints can be relaxed, the resulting problem can be reposed as a second-order cone program (SOCP) which can be solved significantly more efficiently than its SDP counterpart. Simulation results for a team of robots tracking multiple targets are presented.